基于数量化理论Ⅱ的地下矿山矿柱稳定性判别

Pillars' stability assessment in the underground mines based on the quantification theory Ⅱ

矿柱是地下矿山支撑顶板围岩、维持采场稳定的关键结构要素。为迅速准确地判别矿柱稳定性,采用数量化理论II(QTII)建立了地下矿山矿柱稳定性判别模型。选取矿柱宽度、矿柱高度、矿柱宽高比、矿岩单轴抗压强度和矿柱承受载荷作为评价指标,以40组样本数据进行训练,得到了相应的判别系数矩阵,确定了各类样本在5维空间中的中心点和各样本点。利用该模型对训练样本进行回判,判别结果完全正确。用10组样本数据对该判别模型进行检验,结果表明,该模型能较好地判别预测矿柱的稳定性,可以作为一种矿柱稳定性判别工具在工程实践中应用。

This paper is aimed at introducing our research on the pillars stability assessment in the underground coal mine based on the quantification theory II. As is known, it is the pillar that is the key structural elements sustaining the weight of roof rock masses and keeping the stability of the stope in the underground mining. In order to predict the stability of the pillars as efficiently and precisely as possible, we have established an assessment model by taking the advantage of the quantification theory II （QTII）, which is a multivariate statistics analysis method for exploring the unknown properties of the samples based on the known samples. The basic working principle of the method lies in that the failure mechanism of pillars can be clarified with three typical failure models. To do the assessment, we have chosen five indexes for the assessment as the evaluation indictors, which include the width, the height, the ratio of the pillar width to its height, and the uniaxial compressive strength of the rock and the pillar stress. In doing our assessment, first of all, we have to decide the initial matrix of pillar samples. And, secondly, the assessment matrix can be obtained through the mathematical manipulation upon the ini- tial matrix. And, thirdly, the central points of different kinds of pillars （both the stable pillars and the instable pillars）and points in correspondence with the unknown samples in 5-dimensional space can be worked out by multiplying the different matrixes. And, fourthly, the assessment can be done by calculating and comparing the distances between the points corresponding to the unknown samples and the central points of the different kinds of the pillars. If the distance from the point to the central point of the stable pillars is smaller, it would mean that the corresponding samples are stable. If the distance between the point appointed and the central point of the instable pillars is smaller, it would mean that the corresponding samples are instable. Thus, the 40 sets of the pillar samples can be trained ,3ne by one to test the discrimination model. The right-assessment ratio turns out to be 100% . And, in turn, the stability of the left. 10 sets of unknown samples can be predicted by taking the advantage of the as- sessment model. In so doing, the assessment results are supposed to be highly probably accurate and applicable for the actual purpose to be used. Therefore, the assessment model we have developed can be taken as a valuable means in helping to strengthen the safety production of the underground mining.